WASHINGTON - A contrite President Obama announced a rule change to his signature Affordable Care Act on Thursday that will allow insurance companies to keep some of the millions of people who received cancellation notices in recent weeks on their health care plans for another year.

But his proposed fix, which is intended to assist Americans in the individual insurance market who saw their policies canceled because they didn't meet minimum benefit requirements set under the ACA, failed to stanch Republican outrage and only temporarily alleviated Democratic unease over the problems arising from the law's rollout.

"This fix won't solve every problem for every person, but it is going to help a lot of people," said Obama, who has faced criticism because the cancellations came despite his repeated assurances over the past four years that people would be allowed to keep their insurance if they like it.

With Thursday's announcement, Obama hoped to head off Republican lawmakers who have demanded a legislative remedy to the avalanche of cancellation notices - a call that has been joined by uneasy Democrats, including several senators facing tough 2014 re-election battles.

House Republicans are set to vote Friday on legislation sponsored by Fred Upton, R-Mich., to allow people to keep their current, canceled plans. Obama's fix would allow only those whose policies have been canceled in 2013 to re-enroll in their plans for 2014, while the Upton bill would let insurers sell to new customers and, unlike Obama's fix, would not be limited to just one year.

But the White House has dismissed the Upton "Keep Your Health Plan" legislation as designed to undermine the entire ACA by encouraging the healthiest of consumers to enroll in the cheapest, bare-bones plans in the individual market. House Democratic leaders are urging Democrats to oppose it and are crafting an alternative proposal that mirrors the administration's fix. It will not pass because Republicans control the House, but it will give lawmakers a chance to go on record with their position.

Even as he spoke about his plan, the president dispatched senior aides - led by White House chief of staff Denis McDonough - to Capitol Hill to try to ease Democratic lawmakers' concerns and limit the number of House Democrats backing Upton's bill when it comes to a vote.

Frustrations were clear. "Who could be happy with (the roll-out)?" said Rep. Juan Vargas, D-Calif., "The reality is (the administration) didn't do a good job." Still, most Democrats said they remain supportive of the president and the law and that they will need to work harder to make it succeed. "We've just got to be all-in on implementation," said Rep. Peter Welch, D-Vt.

Democrats also put pressure on White House officials to make sure the ongoing problems with the enrollment website, HealthCare.gov, are fixed by the end of the month as the White House has promised. "Getting the website fixed is number one," said Rep. Elijah Cummings, D-Md.

Upton on Thursday dismissed the president's administrative fix as disingenuous.

"Our main priority should be helping the American people," Upton said. "Today's abrupt pivot comes after the White House has spent the last week attacking our thoughtful approach to begin to give peace of mind to those folks worried about losing their affordable health care."

On the Senate side, some Democrats said their concerns were allayed by Obama's fix. But a significant few - including Sens. Mary Landrieu, D-La., Kay Hagan, D-N.C., and Mark Begich, D-Alaska - said they will continue to work for a legislative fix.

Landrieu called the president's actions a good "first step" but said she will continue to push her own legislation - with five Democratic co-sponsors so far - to require insurers to reinstate canceled plans for existing customers and to provide notification letters to consumers on the plans that are available to them. "We will probably need legislation to make it stick," Landrieu said.

However, Senate Democratic leaders remain firmly behind the administration, making a vote on Landrieu's bill unlikely. They are wary of reopening the health care law for debate in a divided Congress where Republicans unanimously oppose the law. Senate Majority Whip Richard Durbin, D-Ill., announced shortly after the meeting with White House officials that there is "no need" for any legislative fixes.

As Obama announced details of his administrative fix at an abruptly called White House news conference, he also lamented his administration's fumbling the roll-out and acknowledged there is "no doubt" the way he repeatedly assured Americans that they would be able to keep their insurance plans "ended up not being accurate."

The president also recognized that his administration's troubled roll-out of the ACA has put a burden on Democrats.

"I feel deeply responsible for making it harder for them rather than easier for them to continue to promote the core values that I think led them to support this thing in the first place," he said.

Senate Democrats control the chamber 55-45, and Republicans intend to use the health care law as a central element in every competitive race in their bid to pick up six seats in 2014.

The Obama fix also relies heavily on insurance providers and state insurance commissioners, who will make the final decision if someone who has received a cancellation notice will be able to keep their current policy.

The insurance industry is regulated at the state level, and the White House confirmed on Thursday that it hadn't received any commitments from state insurance commissioners that they will go along with the president's new policy and approve 2013 policies for next year.

In a speech in Cleveland on Thursday, hours after announcing changes to his signature legislative achievement, Obama vowed he was "not going to gut the law" despite the pressure he faces from Congress

"We're going to fix what needs to be fixed," Obama said. "I am going to see this through."